Results 1 to 9 of 9

Math Help - Numerical Analysis Problem

  1. #1
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Numerical Analysis Problem

    The following data are taken from a polynomial of degree >= 5. What is the polynomial and what is its degree?

    x| -2, -1, 0, 1, 2, 3
    p(x)| -5, 1, 1, 1, 7, 25

    Not sure how to go about finding the poly...

    I know I need to apply Newton's Divided Difference Interpolation Formula some how; I just not sure how? Thanks
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Numerical Analysis Problem

    Quote Originally Posted by jzellt View Post
    The following data are taken from a polynomial of degree >= 5. What is the polynomial and what is its degree?

    x| -2, -1, 0, 1, 2, 3
    p(x)| -5, 1, 1, 1, 7, 25

    Not sure how to go about finding the poly...

    I know I need to apply Newton's Divided Difference Interpolation Formula some how; I just not sure how? Thanks
    You have a typo, the degree cannot be >=5 for a number of reasons, the first is that there is insufficient data (a quintic has 6 degrees of freedom, and you have 6 data points and you can always put a quintic through six points). Secondly it is a perfect fit for a cubic (construct a difference table, the third differences are constant => a cubic).

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Re: Numerical Analysis Problem

    You are absolutely correct! It is supposed to be <=5. Thanks
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Re: Numerical Analysis Problem

    Ok I see that that the third differences are constant and therefore a cubic, but I still don't know how to find the polynomial...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Numerical Analysis Problem

    Quote Originally Posted by jzellt View Post
    Ok I see that that the third differences are constant and therefore a cubic, but I still don't know how to find the polynomial...
    You have already been shown in class how to do that from the difference table, I will not repeat that here.

    Let the cubic be:

    p(x)=ax^3+bx^2+cx+d

    Then you have:

    p(0)=1

    p(1)=1

    p(2)=7

    p(3)=25

    Which when you expand them constitute a set of four simultaneous equations in the four unknowns a,b,c,d.

    CB
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Re: Numerical Analysis Problem

    Thank you! But wouldn't p(0) = -5?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Numerical Analysis Problem

    Quote Originally Posted by jzellt View Post
    Thank you! But wouldn't p(0) = -5?
    Code:
    x   | -2,-1, 0, 1, 2, 3
    p(x)| -5, 1, 1, 1, 7, 25
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Super Member
    Joined
    Feb 2008
    Posts
    535

    Re: Numerical Analysis Problem

    Pardon me. My mistake. What I meant to say is why leave out p(-2) and p(-1)? Thanks
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Numerical Analysis Problem

    Quote Originally Posted by jzellt View Post
    Pardon me. My mistake. What I meant to say is why leave out p(-2) and p(-1)? Thanks
    You only need four equations. You can choose any four

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Numerical Analysis Interpolation problem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: October 16th 2011, 07:45 PM
  2. Numerical analysis problem
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: February 22nd 2009, 12:19 PM
  3. Numerical analysis (approximation) problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: June 8th 2008, 11:52 AM
  4. Numerical Analysis problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: April 12th 2008, 05:24 PM
  5. Numerical Analysis problem
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: April 10th 2008, 03:44 PM

Search Tags


/mathhelpforum @mathhelpforum